The symmetric Tucker decomposition of moment tensors has other motivations, besides compression.
In some scientific domains, one encounters data having high volatility, e.g., in combustion simulations [1]}, outlier detection [2]}, [3]} and financial asset allocation [4]}, [5]}, [6]}.
Moments and cumulants (\(d \ge 3\) ) are sensitive to heavy tails and anomalies.
Thus, as principal component analysis (PCA) and the covariance matrix are well-suited to Gaussian data, finding the key subspaces of variability in higher-order statistics is necessary for non-normal data analysis.
These subspaces are found by computing the low-rank symmetric Tucker approximation.
